# Effective potentials and basis sets

Group # | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | ||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Period | ||||||||||||||||||||

1 | 1 H |
2 He |
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2 | 3 Li |
4 Be |
5 B |
6 C |
7 N |
8 O |
9 F |
10 Ne |
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3 | 11 Na |
12 Mg |
13 Al |
14 Si |
15 P |
16 S |
17 Cl |
18 Ar |
||||||||||||

4 | 19 K |
20 Ca |
21 Sc |
22 Ti |
23 V |
24 Cr |
25 Mn |
26 Fe |
27 Co |
28 Ni |
29 Cu |
30 Zn |
31 Ga |
32 Ge |
33 As |
34 Se |
35 Br |
36 Kr |
||

5 | 37 Rb |
38 Sr |
39 Y |
40 Zr |
41 Nb |
42 Mo |
43 Tc |
44 Ru |
45 Rh |
46 Pd |
47 Ag |
48 Cd |
49 In |
50 Sn |
51 Sb |
52 Te |
53 I |
54 Xe |
||

6 | 55 Cs |
56 Ba |
* |
72 Hf |
73 Ta |
74 W |
75 Re |
76 Os |
77 Ir |
78 Pt |
79 Au |
80 Hg |
81 Tl |
82 Pb |
83 Bi |
84 Po |
85 At |
86 Rn |
||

7 | 87 Fr |
88 Ra |
** |
104 Rf |
105 Db |
106 Sg |
107 Bh |
108 Hs |
109 Mt |
110 Ds |
111 Rg |
112 Cn |
113 Nh |
114 Fl |
115 Mc |
116 Lv |
117 Ts |
118 Og |
||

8 | 119 |
120 |
*** |
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* Lanthanides |
57 La |
58 Ce |
59 Pr |
60 Nd |
61 Pm |
62 Sm |
63 Eu |
64 Gd |
65 Tb |
66 Dy |
67 Ho |
68 Er |
69 Tm |
70 Yb |
71 Lu |
|||||

** Actinides |
89 Ac |
90 Th |
91 Pa |
92 U |
93 Np |
94 Pu |
95 Am |
96 Cm |
97 Bk |
98 Cf |
99 Es |
100 Fm |
101 Md |
102 No |
103 Lr |
|||||

*** | 121 |
122 |

Our group proposed a generalization of the "shape-consistent" Effective Core Potential (ECP) method (which is widely used in the electronic structure calculations of molecules with heavy atoms) for both nonrelativistic [1,2] and relativistic cases [3,4]. In these papers, the widespread conception about necessity of the "shape-consistent" ECP generation for the nodeless pseudoorbitals (to avoid the singularities when inverting the Hartree-Fock equations) was overcome, and the outermost core pseudoorbitals together with the valence pseudoorbitals which may have nodes were included in the ECP generation scheme for the use in precise calculations.

It was shown that the difference between the valence and outer core effective potentials with the same angular (l) and total (j) electronic momenta should be taken into account to perform precise Relativistic ECP (RECP) calculations, and a new (Generalized RECP or GRECP) operator including non-local terms with the projectors on the outer core pseudospinors additionally to the conventional semi-local RECP operator was proposed. These correcting terms are especially important for accurate simulation of interactions with the valence electrons [3,4].

Test atomic numerical self-consistent field calculations [4,5] demonstrated
that such a modification of the original semi-local RECP operator permited to increase the accuracy
of simulation of an atomic Hamiltonian about 10 times in the valence region when reducing 2-3 times
the radii of the atomic core regions where orbitals are smoothed by any manner. Then the calculations
with accounting for the correlation effects on the Hg and Pb atoms [6,7] confirmed high accuracy of
the GRECP method in reproducing the all-electron relativistic results. The good agreement of
the experimental spectroscopic constants with the results
of the GRECP correlation calculations on the HgH and Ca_{2} molecules [8,9] also shown reliability of
the GRECP method.

Accounting of contribution from Breit interactions in the framework of the GRECP method was considered in [8,10]. The theory of the GRECP approach is presented in [11]. The reviews of the GRECP method can be found in [12,13,14].